N. Sule, K. J. Willis, S. C. Hagness, and I. Knezevic
https://journals.aps.org/prb/accepted/f1076O3dG0313f2b82308c24eff2c3c243647ae6a
We calculate the room-temperature complex conductivity \sigma(\omega) of suspended and supported graphene at terahertz frequencies (100\,{\mathrm{GHz}}\text{--}10\,{\mathrm{THz}}) by employing a self-consistent coupled simulation of carrier transport and electrodynamics. We consider a wide range of electron (n=1012\text{--}\,1013\,{\mathrm{cm}-2}) and impurity densities ( N\mathrm{i}=8\times 1010\text{--}\, 2\times 1012\,{\mathrm{cm}-2}). For graphene supported on SiO2, there is excellent agreement between the calculation with clustered impurities and the experimentally measured \sigma(\omega). The choice of substrate (SiO2 or h-BN) is important at frequencies below 4 THz. We show that carrier scattering with substrate phonons governs transport in supported graphene for N\mathrm{i}/n0.1, and transport enters the electron-hole puddle regime for N\mathrm{i}/n>0.5. The simple Drude model, with an effective scattering rate \Gamma and Drude weight D as parameters, fits the calculated \sigma (\omega) for supported graphene very well, owing to electron-impurity scattering. \Gamma decreases with increasing n faster than n-1/2 and is insensitive to electron-electron interaction. Both electron-electron and electron-impurity interactions reduce the Drude weight D, and its dependence on n is sublinear.
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